{"product_id":"geometry-of-principal-sheaves-von-efstathios-vassiliou","title":"Geometry of Principal Sheaves","description":"\u003cp\u003eL¿ inj¿ ¿ enuit¿ ¿ m¿ eme d¿ un regard neuf (celui de la science l¿est toujours) peut parfois ¿ ¿clairer d¿ un jour nouveau d¿ anciens probl` emes. J.Monod [77, p. 13] his book is intended as a comprehensive introduction to the theory of T principalsheaves andtheirconnections inthesettingofAbstractDi?- ential Geometry (ADG), the latter being initiated by A. Mallios¿sGeometry of Vector Sheaves [62]. Based on sheaf-theoretic methods and sheaf - homology, the presentGeometry of Principal Sheaves embodies the classical theory of connections on principal and vector bundles, and connections on vector sheaves, thus paving the way towards a uni?ed (abstract) gauge t- ory and other potential applications to theoretical physics. We elaborate on the aforementioned brief description in the sequel. Abstract (ADG) vs. Classical Di?erential Geometry (CDG). M- ern di?erential geometry is built upon the fundamental notions of di?er- tial (smooth) manifolds and ?ber bundles, based,intheir turn, on ordinary di?erential calculus. However, the theory of smooth manifolds is inadequate to cope, for - stance, with spaces like orbifolds, spaces with corners, or other spaces with more complicated singularities. This is a rather unfortunate situation, since one cannot apply the powerful methods of di?erential geometry to them or to any spaces that do not admit an ordinary method of di?erentiation. The ix x Preface same inadequacy manifests in physics, where many geometrical models of physical phenomena are non-smooth.\u003c\/p\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9789048168583\"\u003e\u003ch3\u003e\u003c\/h3\u003e\u003c\/div\u003e","brand":"Libri","offers":[{"title":"Softcover - 9789048168583","offer_id":39416649678941,"sku":"9789048168583","price":106.99,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/6a2e41f4-7da1-4ac0-8d30-b5976304b23f.jpg?v=1772262923","url":"https:\/\/shop.autorenwelt.de\/products\/geometry-of-principal-sheaves-von-efstathios-vassiliou","provider":"Autorenwelt Shop","version":"1.0","type":"link"}